Binary strip position resolution (${\sigma }_x=w/\sqrt{12}$)

If a single strip of pitch $w$ reports only its centre and the impact position has a uniform distribution, the position error is uniform on $[-w/2,w/2]$. Its variance is $w^{-1}{\int }_{-w/2}^{w/2}{x}^{2}dx=w^2/12$. Charge sharing and analogue readout can improve this resolution.